#7266 closed enhancement (fixed)
implement computation of Silverman height bounds
Reported by: | was | Owned by: | was |
---|---|---|---|
Priority: | major | Milestone: | sage-4.2.1 |
Component: | number theory | Keywords: | |
Cc: | robertwb cremona | Merged in: | sage-4.2.1.alpha0 |
Authors: | William Stein | Reviewers: | Robert Bradshaw |
Report Upstream: | Work issues: | ||
Branch: | Commit: | ||
Dependencies: | Stopgaps: |
Description
The Silverman height bound isn't necessarily as tight at the CPS bound, but it works uniformly over all field extensions, which makes it very useful for some applications, e.g., computing mordell-weil groups over number fields. So let's add it to Sage!
Attachments (1)
Change History (7)
Changed 8 years ago by
comment:1 Changed 8 years ago by
- Status changed from new to needs_review
comment:2 Changed 8 years ago by
comment:3 follow-up: ↓ 4 Changed 8 years ago by
- Status changed from needs_review to positive_review
Looks good to me. It's a simple enough formula that I'd say the redundant implementation is worth it if just for the ease of introspection.
We're looking at using this for provable computations of Heegner points, where the field of definition is not a priori known.
comment:4 in reply to: ↑ 3 Changed 8 years ago by
Replying to robertwb:
Looks good to me. It's a simple enough formula that I'd say the redundant implementation is worth it if just for the ease of introspection.
We're looking at using this for provable computations of Heegner points, where the field of definition is not a priori known.
Fair point(s). One reason for getting better (usually) bounds for *rational* points via the CPS method is precisely due to this restriction. I have no objection!
comment:5 Changed 8 years ago by
- Merged in set to sage-4.2.1.alpha0
- Resolution set to fixed
- Reviewers set to Robert Bradshaw
- Status changed from positive_review to closed
comment:6 Changed 8 years ago by
But I read here that the Sage project "religiously avoiding redundant code.": http://www.metafilter.com/86262/unbump
Is there any particular reason for using a native Sage implementation instead of using mwrank/eclib?
I know that #360 has still not been done, but I can't quite see the point of this patch for curves over Q.